﻿<p>An <em>IfcEdge</em> defines two vertices being connected topologically. The geometric representation of the connection between the two vertices defaults to a straight line if no curve geometry is assigned using the subtype <em>IfcEdgeCurve</em>. The <em>IfcEdge</em> can therefore be used to exchange straight edges
without an associated geometry provided by <em>IfcLine</em> or <em>IfcPolyline</em> thought <em>IfcEdgeCurve.EdgeGeometry</em>.</p>
<p>&nbsp;</p>
<table>
<tr><td><br><img src="../../../figures/ifcedge.png" alt="edge representation" border="0"></td>
<td><blockquote class="example">EXAMPLE&nbsp; Figure 2 illustrates an example where the bounds of the <em>IfcEdge</em> are given by the <em>EdgeStart</em> and <em>EdgeEnd</em>; this also determines the direction of the edge. The location within a coordinate space is determined by the <em>IfcVertexPoint</em> type for <em>EdgeStart</em> and <em>EdgeEnd</em>. Since no edge geometry is assigned, it defaults to a straight line agreeing to the direction sense.</blockquote></td>
</tr>
<tr><td><p class="figure">Figure 2 &mdash; Edge representation</p></td><td>&nbsp;</td></tr>
</table>

<p>&nbsp;</p>
<blockquote class="extDef">NOTE&nbsp; Definition according to ISO/CD 10303-42:1992<br>
An edge is the topological construct corresponding to the connection of two
vertices. More abstractly, it may stand for a logical relationship between two vertices. The domain of an edge, if
present, is a finite, non-self-intersecting open curve in <em>R<sup>M</sup></em>, that is, a connected 1-dimensional
manifold. The bounds of an edge are two vertices, which need not be distinct. The edge is oriented by choosing its traversal
direction to run from the first to the second vertex. If the two vertices are the same, the edge is a self loop. The domain of the
edge does not include its bounds, and 0 &le; &Xi; &le; &infin;. Associated with an edge may be a geometric curve to locate the
edge in a coordinate space; this is represented by the edge curve subtype. The curve shall be finite and non-self-intersecting within 
the domain of the edge. An edge is a graph, so its multiplicity M and graph genus <em>G<sup>e</sup></em> may be determined by the 
graph traversal algorithm. Since <em>M</em> = <em>E</em> = 1, the Euler equation (1) reduces in the case to:
<blockquote><img src="../../../figures/ifcedge-math1.gif" width="105" height="24"></blockquote>
where <em>V</em> = 1 or 2, and <em>G<sup>e</sup></em> = 1 or 0. Specifically, the topological edge defining data shall satisfy:
<ul>
<li class="extDef">an edge has two vertices <br><img src="../../../figures/ifcedge-math2.gif" width="64" height="26"></li>
<li class="extDef">the vertices need not be distinct <br><img src="../../../figures/ifcedge-math3.gif" width="88" height="26"></li>
<li class="extDef">Equation shall hold <br><img src="../../../figures/ifcedge-math4.gif" width="120" height="26"></li>
</ul>
</blockquote>
<blockquote class="note">NOTE&nbsp; Entity adapted from <strong>edge</strong> defined in ISO 10303-42.</blockquote>
<blockquote class="history">HISTORY&nbsp; New entity in IFC2.0</blockquote>

<p class="spec-head">Informal Propositions:</p>
<ol>
<li>The edge has dimensionality 1.</li>
<li>The extent of an edge shall be finite and nonzero.</li>
</ol>